ARMARKOV least-squares identification

Akers, James C.; Bernstein, Dennis S.

doi:10.1109/acc.1997.611782

Cited by 25 publications

(9 citation statements)

References 4 publications

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“…Akers & Bernstein (1997) showed that the Markov parameters can be extracted from the ARX representation via the following recursive algorithm. Using (2.5) and the definition of the measurement y we obtain, after repeated substitution, the following auto-regressive representation that explicitly isolates µ Markov parameters (referred to as µ-ARMarkov):…”

Section: General Framework For Linear Time-invariant Systems (Lti)mentioning

confidence: 99%

“…The transfer functions based on the z-transform of the above models (FIR, ARMA and µ-ARMarkov) are given in the appendix for completeness. The following section presents the algorithm proposed by Akers & Bernstein (1997) to identify the µ-ARMarkov parameters (in W) from input-output data sequences. Once the Markov parameters are identified (as a part of the vector W), the system behavior is predicted using the FIR model (2.4).…”

Section: General Framework For Linear Time-invariant Systems (Lti)mentioning

confidence: 99%

“…The Markov parameters are then used in the Eigensystem Realization Algorithm (ERA) to arrive at a state-space representation of the model, which in turn can be used to design a control law by standard techniques. The ARMarkov/LS procedure has originally been proposed by Akers & Bernstein (1997), and many subsequent studies (see Van Pelt & Bernstein 1998;Kamrunnahar et al 2000;Fledderjohn et al 2010) have confirmed it as a very efficient technique to obtain the Markov parameters of a system. The ERA state-space realization step has been developed by Juang & Pappa (1985), has been studied extensively (see Lew et al 1993) and has recently been applied to flow control problems in the form of an adjoint-free model reduction procedure (see Ma et al 2011).…”

Section: Introductionmentioning

confidence: 99%

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Uncertainty propagation in model extraction by system identification and its implication for control design

Dovetta

Schmid

Sipp³

2016

J. Fluid Mech.

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In data-based control design, system-identification techniques are used to extract lowdimensional representations of the input-output map between actuators and sensors from observed data-signals. Under realistic conditions, noise in the signals is present and is expected to influence the identified system representation. For the subsequent design of the controller, it is important to gauge the sensitivity of the system representation to noise in the observed data; this information will impact the robustness of the controller and influence the stability margins for a closed-loop configuration. Commonly, Monte-Carlo analysis has been used to quantify the effect of data-noise on the system identification and control design, but in fluid systems, this approach is often prohibitively expensive, both for numerical simulations and physical experiments. Instead, we present a framework for the estimation of statistical properties of identified system representations given an uncertainty in the processed data. The ARMarkov/LS identification procedure has been chosen to illustrate this framework and to obtain error bounds on the identified system parameters based on the signal-to-noise ratio of the input-output data sequence. Multiple simulations (as in Monte-Carlo techniques) are not necessary, which makes the proposed technique affordable and efficient even for large-scale flow control problems. The procedure is illustrated on the control design for flow over an idealized airfoil with a trailing-edge splitter plate.

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Section: General Framework For Linear Time-invariant Systems (Lti)mentioning

confidence: 99%

Section: General Framework For Linear Time-invariant Systems (Lti)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Uncertainty propagation in model extraction by system identification and its implication for control design

Dovetta

Schmid

Sipp³

2016

J. Fluid Mech.

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“…The ARMARKOV algorithm is applied to various experimental testbeds in [32]- [41] and is demonstrated on fluid dynamic systems in [26], [27].…”

Section: Adaptive Disturbance Rejection Algorithmmentioning

confidence: 99%

Adaptive Disturbance Rejection for Flow in a Duct with Time-Varying Upstream Velocity

Santillo

Hoagg

Bernstein

et al. 2007

2007 American Control Conference

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In this paper we demonstrate adaptive flow control for an incompressible viscous fluid through a two-dimensional channel without using an analytical model. An adaptive disturbance rejection algorithm is implemented within a CFD simulation to reduce the effects of an unknown time-varying inlet velocity disturbance on the performance variable, which is the longitudinal velocity component of the flow at a downstream location. The algorithm requires minimal knowledge of the system, specifically, the numerator coefficients of the transfer functions from the control inputs to the performance variable. System identification, based on CFD simulation prior to disturbance rejection, is used to identify the required parameters.

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“…In this research, r is set to be equal to s for convenience. Then, we apply the singular value decomposition as describe in Akers and Bernstein (1997A) Hr,so =PSr,, Q T…”

Section: Armarkovals/era Algorithmmentioning

confidence: 99%

Separation Control Using ZNMF Devices: Flow Physics and Scaling Laws

Tian¹,

Cattafesta²

2007

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20080604029 REPORT DOCUMENTATION PAGE Form Approved I OMB No. 0704-0188Public reporting burden for this collection of information is estimated to average hour per response, including the time for reviewing instructions, searching data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to

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ARMARKOV least-squares identification

Cited by 25 publications

References 4 publications

Uncertainty propagation in model extraction by system identification and its implication for control design

Uncertainty propagation in model extraction by system identification and its implication for control design

Adaptive Disturbance Rejection for Flow in a Duct with Time-Varying Upstream Velocity

Separation Control Using ZNMF Devices: Flow Physics and Scaling Laws

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